The “simple” explanation for this special name for the last day of Chanuka is the Torah reading from the end of Parshat Naso that emphatically announces ZOT CHANUKAT HA-MIZBEI’ACH (when the Torah is summing up the gifts of all the Tribal Leaders.
There is another, deeper meaning to the name. If you want to really know what Chanukah is all about, the answer is THIS, THE EIGHTH DAY OF CHANUKAH – the fact that there are 8 days of Chanukah – ZOT CHANUKAH, this is what Chanukah means. It means EIGHT. EIGHT is our answer to the Greek challenge. They said nature is perfect. They said it is a mutilation of the body to be circumcised. And they forbid us to fulfill that great mitzva of ours, under pain of death. EIGHT represents the step beyond TEVA, beyond nature. MILA on the 8th day represents our challenge to go beyond how we were created and take charge of the completion of our physical and spiritual form. The Mikdash began to function on its higher spiritual level on the EIGHTH day. The Greeks tried to take that away from us too. Torah was given to us on the day following seven sevens. It is an EIGHTH too. And the Greeks tried to take that from us also. With G-d’s help, we prevailed over the Greeks and the triumph is celebrated with an 8 day holiday. This is Chanukah. ZOT CHANUKAH.